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Class 7 Maths Worksheet: Triangles

Maths worksheets lesson 53: Triangles: angle sum, exterior angle and Pythagoras · Set 461 · 40 sums
TalentJR

The method (Inside 180, outside the sum): Angle sum: ∠A + ∠B + ∠C = 180°. Exterior angle = sum of the two interior opposite angles. Right-angled triangle: longest side² = side² + side² (3, 4, 5 and 5, 12, 13 are famous sets). Sides can make a triangle only if the two shorter sides add up to more than the longest side.

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  1. 1.The two shorter sides of a right-angled triangle are 8 cm and 15 cm. How long is the longest side (in cm)?
  2. 2.The angles of a triangle are in the ratio 1 : 4 : 5. What is the smallest angle (in degrees)?
  3. 3.In a right-angled triangle, one of the other two angles is 14°. What is the third angle (in degrees)?
  4. 4.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles (in degrees)?
  5. 5.In triangle ABC, angle A = 99° and angle B = 40°. What is angle C (in degrees)?
  6. 6.In triangle ABC, angle A = 37° and angle B = 112°. What is angle C (in degrees)?
  7. 7.The angles of a triangle are in the ratio 3 : 4 : 5. What is the biggest angle (in degrees)?
  8. 8.In a right-angled triangle, one of the other two angles is 57°. What is the third angle (in degrees)?
  9. 9.In triangle ABC, angle A = 67° and angle B = 21°. What is angle C (in degrees)?
  10. 10.In triangle ABC, angle A = 23° and angle B = 25°. What is angle C (in degrees)?
  11. 11.The angles of a triangle are in the ratio 2 : 3 : 5. What is the biggest angle (in degrees)?
  12. 12.The longest side of a right-angled triangle is 39 cm and one of the other sides is 15 cm. How long is the third side (in cm)?
  13. 13.In an isosceles triangle, the two equal angles are 82° each. What is the third angle (in degrees)?
  14. 14.The longest side of a right-angled triangle is 13 cm and one of the other sides is 5 cm. How long is the third side (in cm)?
  15. 15.Can a triangle have sides of 5 cm, 8 cm and 5 cm? (a) No (b) Yes
  16. 16.In triangle ABC, angle A = 49° and angle B = 54°. What is angle C (in degrees)?
  17. 17.In a right-angled triangle, one of the other two angles is 27°. What is the third angle (in degrees)?
  18. 18.In a right-angled triangle, one of the other two angles is 19°. What is the third angle (in degrees)?
  19. 19.In an isosceles triangle, the angle between the two equal sides is 68°. What is each of the other two angles (in degrees)?
  20. 20.An exterior angle of a triangle is 98°. One of its two interior opposite angles is 20°. What is the other one (in degrees)?
  21. 21.In an isosceles triangle, the angle between the two equal sides is 52°. What is each of the other two angles (in degrees)?
  22. 22.In a right-angled triangle, one of the other two angles is 39°. What is the third angle (in degrees)?
  23. 23.The angles of a triangle are in the ratio 2 : 3 : 4. What is the biggest angle (in degrees)?
  24. 24.In triangle ABC, angle A = 65° and angle B = 29°. What is angle C (in degrees)?
  25. 25.Can a triangle have sides of 7 cm, 7 cm and 13 cm? (a) No (b) Yes
  26. 26.The angles of a triangle are in the ratio 2 : 2 : 5. What is the smallest angle (in degrees)?
  27. 27.In triangle ABC, angle A = 76° and angle B = 56°. What is angle C (in degrees)?
  28. 28.The two shorter sides of a right-angled triangle are 18 cm and 24 cm. How long is the longest side (in cm)?
  29. 29.The angles of a triangle are in the ratio 1 : 2 : 6. What is the smallest angle (in degrees)?
  30. 30.In a right-angled triangle, one of the other two angles is 17°. What is the third angle (in degrees)?
  31. 31.In a right-angled triangle, one of the other two angles is 60°. What is the third angle (in degrees)?
  32. 32.The two shorter sides of a right-angled triangle are 20 cm and 15 cm. How long is the longest side (in cm)?
  33. 33.Can a triangle have sides of 14 cm, 2 cm and 11 cm? (a) No (b) Yes
  34. 34.In triangle ABC, angle A = 28° and angle B = 118°. What is angle C (in degrees)?
  35. 35.An exterior angle of a triangle is 106°. One of its two interior opposite angles is 63°. What is the other one (in degrees)?
  36. 36.In an isosceles triangle, the two equal angles are 66° each. What is the third angle (in degrees)?
  37. 37.The longest side of a right-angled triangle is 15 cm and one of the other sides is 12 cm. How long is the third side (in cm)?
  38. 38.In an isosceles triangle, the angle between the two equal sides is 22°. What is each of the other two angles (in degrees)?
  39. 39.In a right-angled triangle, one of the other two angles is 25°. What is the third angle (in degrees)?
  40. 40.The angles of a triangle are in the ratio 1 : 2 : 2. What is the smallest angle (in degrees)?

Answer key

  1. 17
  2. 18
  3. 76
  4. 45
  5. 41
  6. 31
  7. 75
  8. 33
  9. 92
  10. 132
  11. 90
  12. 36
  13. 16
  14. 12
  15. Yes
  16. 77
  17. 63
  18. 71
  19. 56
  20. 78
  21. 64
  22. 51
  23. 80
  24. 86
  25. Yes
  26. 40
  27. 48
  28. 30
  29. 20
  30. 73
  31. 30
  32. 25
  33. No
  34. 34
  35. 43
  36. 48
  37. 9
  38. 79
  39. 65
  40. 36

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